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High School Physics : Calculating Momentum

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Example Question #11 : Calculating Momentum

A 117kg crate slides along a floor with a starting velocity of $21\frac{m}{s}$ . If the force due to friction is -330N , how long will it take before the crate slides to a stop?

Possible Answers:

14.5

6.6s

11.2s

7.5s

9.2s

Correct answer:

7.5s

Explanation:

The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: p=mv . We can rewrite this equation in terms of force.

$mv=(kg)(\frac{m}{s})=(kg)(\frac{m}{s})*(\frac{s}{s})$

$\frac{kg*m}{s^2}*s=N*s=Ft$

Using this transformation, we can see that momentum is also equal to force times time.

$\Delta p=F\Delta t$ can also be thought of as $(p_{final}-p_{initial})=F\Delta t$ .

Expand this equation to include our given values.

$(mv_{final}-mv_{initial})=F\Delta t$

Since the crate is not moving at the end, its final velocity is zero. Plug in the given values and solve for the time.

$(117kg* 0\frac{m}{s})-(117kg* 21\frac{m}{s})=-330N* \Delta t$

$-(117kg* 21\frac{m}{s})=-330N* \Delta t$

$(-2457\frac{kg\cdot m}{s})=-330N* \Delta t$

$\frac{(-2457\frac{kg\cdot m}{s})}{-330N}= \Delta t$

$7.5s= \Delta t$

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Example Question #12 : Calculating Momentum

Courtney pushes a car 1200kg with 40N of force along a frictionless surface. If the car is initially at rest, how long does she need to push for the car to reach a velocity of $10\frac{m}{s}$ ?

Possible Answers:

150s

500s

300s

600s

200s

Correct answer:

300s

Explanation:

The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: p=mv . We can rewrite this equation in terms of force.

$mv=(kg)(\frac{m}{s})=(kg)(\frac{m}{s})*(\frac{s}{s})$

$\frac{kg*m}{s^2}*s=N*s=Ft$

Using this transformation, we can see that momentum is also equal to force times time.

$\Delta p=F\Delta t$ can also be thought of as $(p_{final}-p_{initial})=F\Delta t$ .

Expand this equation to include our given values.

$(mv_{final}-mv_{initial})=F\Delta t$

Since the car is not moving at the beginning, its initial velocity is zero. Plug in the given values and solve for the time.

$(1200kg* 10\frac{m}{s})-(1200kg* 0\frac{m}{s})=(40N)\Delta t$

$12000\frac{kg\cdot m}{s}=(40N) \Delta t$

$\frac{12000\frac{kg\cdot m}{s}}{40N}=\Delta t$

$300s=\Delta t$

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Example Question #13 : Calculating Momentum

A 0.05kg ball hits a brick wall with a velocity of $9.7\frac{m}{s}$ and bounces back at the same speed. If the ball is in contact with the wall for 0.2s , what is the value of the force exerted by the wall on the ball?

Possible Answers:

-5.98N

-9.70N

-4.35N

-19.40N

-4.85N

Correct answer:

-4.85N

Explanation:

The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: p=mv . We can rewrite this equation in terms of force.

$mv=(kg)(\frac{m}{s})=(kg)(\frac{m}{s})*(\frac{s}{s})$

$\frac{kg*m}{s^2}*s=N*s=Ft$

Using this transformation, we can see that momentum is also equal to force times time.

$\Delta p=F\Delta t$ can also be thought of as $(p_{final}-p_{initial})=F\Delta t$ .

Expand this equation to include our given values.

$(mv_{final}-mv_{initial})=F\Delta t$

Even though the ball is bouncing back at the same "speed", its velocity will now be negative as it is moving in the opposite direction. Using what we know from the question, we can solve for the force.

$(0.05kg*-9.7\frac{m}{s})-(0.05kg* 9.7\frac{m}{s})=F(0.2s)$

$(-0.485\frac{kg\cdot m}{s})-(0.485\frac{kg\cdot m}{s})=F(0.2s)$

$(-0.97\frac{kg\cdot m}{s})=F(0.2s)$

$\frac{(-0.97\frac{kg\cdot m}{s})}{0.2s}=F$

-4.85N=F

Our answer is negative because the force is acting on the ball in the OPPOSITE direction from the way it was originally heading.

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Example Question #14 : Calculating Momentum

A 0.75kg ball strikes a 2.5kg ball at rest. After the collision the 0.75kg ball is moving with a velocity of $20\frac{m}{s}$ and the second ball is moving with a velocity of $22\frac{m}{s}$ . What is the initial velocity of the first ball?

Possible Answers:

$83.67\frac{m}{s}$

$93.33\frac{m}{s}$

$99.25\frac{m}{s}$

$101.33\frac{m}{s}$

$55.17\frac{m}{s}$

Correct answer:

$93.33\frac{m}{s}$

Explanation:

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy.

We can use the law of conservation of momentum to equate the initial and final terms.

$m_1v_{1initial}+m_2v_{2initial}=m_1v_{1final}+m_2v_{2final}$

Plug in the given values and solve for $\small v_{1initial}$ .

$(0.75kg*v_{1initial})+(2.5kg* 0\frac{m}{s})=(0.75kg*20\frac{m}{s})+(2.5kg* 22\frac{m}{s})$

$(0.75kg* v_{1initial})+(0)=(15\frac{kg\cdot m}{s} )+(55\frac{kg\cdot m}{s})$

$(0.75kg* v_{1initial})=(70\frac{kg\cdot m}{s} )$

$v_{1initial}=\frac{70\frac{kg\cdot m}{s}}{0.75kg}$

$v_{1initial}=93.33\frac{m}{s}$

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Example Question #15 : Calculating Momentum

A 0.05kg ball strikes a piece of paper moving at $40\frac{m}{s}$ . It breaks through the paper and continues in the same direction. If the paper exerted a force of -18N on the ball and the two are in contact for 0.01s , what is the final momentum of the ball?

Possible Answers:

$1.13\frac{kg\cdot m}{s}$

$3.64\frac{kg\cdot m}{s}$

$0.91\frac{kg\cdot m}{s}$

$2.42\frac{kg\cdot m}{s}$

$1.82\frac{kg\cdot m}{s}$

Correct answer:

$1.82\frac{kg\cdot m}{s}$

Explanation:

The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: p=mv . We can rewrite this equation in terms of force.

$mv=(kg)(\frac{m}{s})=(kg)(\frac{m}{s})*(\frac{s}{s})$

$\frac{kg*m}{s^2}*s=N*s=Ft$

Using this transformation, we can see that momentum is also equal to force times time.

$\Delta p=F\Delta t$ can also be thought of as $(p_{final}-p_{initial})=F\Delta t$ .

Since we are solving for $p_{final}$ , we can leave that part of the equation alone and expand the rest to include our given values.

$p_{final}-mv_{initial}=F\Delta t$

From here, plug in the given values and solve for the final momentum.

$p_{final}-(0.05kg*40\frac{m}{s})=(-18N)(0.01s)$

$p_{final}-(2\frac{kg\cdot m}{s})=(-0.18N\cdot s)$

At this point, remember that $1N=1\frac{kg\cdot m}{s^2}$ to see that both sides are now working in the same units.

$p_{final}=-0.18\frac{kg\cdot m}{s}+2\frac{kg\cdot m}{s}$

$p_{final}=1.82\frac{kg\cdot m}{s}$

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Example Question #16 : Calculating Momentum

A 12kg ball moving at $76.4\frac{m}{s}$ strikes a second ball at rest. After the collision the 12kg ball is moving with a velocity of $22.2\frac{m}{s}$ and the second ball is moving with a velocity of $13.7\frac{m}{s}$ . What is the mass of the second ball?

Possible Answers:

31.2kg

29.3kg

45.8kg

92.3kg

11.7kg

Correct answer:

29.3kg

Explanation:

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy.

We can use the law of conservation of momentum to equate the initial and final terms.

$m_1v_{1initial}+m_2v_{2initial}=m_1v_{1final}+m_2v_{2final}$

Plug in the given values and solve for $\small m_2$ .

$(12kg*76.4\frac{m}{s})+(m_2*0\frac{m}{s})=(12kg* 22.2\frac{m}{s})+(m_2* 13.7\frac{m}{s})$

$(916.8\frac{kg\cdot m}{s})+(0)=(266.4\frac{kg\cdot m}{s})+m_2(22.2\frac{m}{s})$

$(916.8\frac{kg\cdot m}{s})-(266.4\frac{kg\cdot m}{s})=m_2(22.2\frac{m}{s})$

$(650.4\frac{kg\cdot m}{s})=m_2( 22.2\frac{m}{s})$

$\frac{650.4\frac{kg\cdot m}{s}}{22.2\frac{m}{s}}=m_2$

29.3kg=m_2

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Example Question #12 : Calculating Momentum

A 3400kg car travelling at $28.7\frac{m}{s}$ rear ends another 3400kg car at rest. The two bumpers lock and the cars move forward together. What is their final velocity?

Possible Answers:

$15.1\frac{m}{s}$

$28.7\frac{m}{s}$

$13.3\frac{m}{s}$

$19.5\frac{m}{s}$

$14.4\frac{m}{s}$

Correct answer:

$14.4\frac{m}{s}$

Explanation:

This is an example of an inelastic collision, as the two cars stick together after colliding. We can assume momentum is conserved.

To make the equation easier, let's call the first car "1" and the second car "2."

Using conservation of momentum and the equation for momentum, p=mv , we can set up the following equation.

$m_1v_{1initial}+m_2v_{2initial}=(m_1+m_2)v_{final}$

Since the cars stick together, they will have the same final velocity. We know the second car starts at rest, and the velocity of the first car is given. Plug in these values and solve for the final velocity.

$(3400kg* 28.7\frac{m}{s})+(3400kg*0\frac{m}{s})=(3400kg+3400kg)v_{final}$

$97580\frac{kg\cdot m}{s}=(6800kg)v_{final}$

$\frac{97580\frac{kg\cdot m}{s}}{6800kg}=v_{final}$

$14.4\frac{m}{s}=v_{final}$

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Example Question #13 : Calculating Momentum

A 950kg strikes a 2200kg car at rest from behind. The bumpers lock and they move forward together. If the final velocity of the joined cars is equal to $15\frac{m}{s}$ , what was the initial speed of the first car?

Possible Answers:

$50.2\frac{m}{s}$

$71.2\frac{m}{s}$

$46.2\frac{m}{s}$

$49.7\frac{m}{s}$

$33.2\frac{m}{s}$

Correct answer:

$49.7\frac{m}{s}$

Explanation:

This is an example of an inelastic collision, as the two cars stick together after colliding. We can assume momentum is conserved.

To make the equation easier, let's call the first car "1" and the second car "2."

Using conservation of momentum and the equation for momentum, p=mv , we can set up the following equation.

$m_1v_{1initial}+m_2v_{2initial}=(m_1+m_2)v_{final}$

Since the cars stick together, they will have the same final velocity. We know the second car starts at rest, and the final velocity of the joined cars is given. Plug in these values and solve for the initial velocity of the first car.

$(950kg*v_{1initial})+(2200kg* 0\frac{m}{s})=(950kg+2200kg)* 15\frac{m}{s}$

$950kg* v_{1initial}=(3150kg)*15\frac{m}{s}$

$950kg* v_{1initial}=47250\frac{kg\cdot m}{s}$

$v_{1initial}=\frac{47250\frac{kg\cdot m}{s}}{950kg}$

$v_{1initial}=49.7\frac{m}{s}$

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Example Question #17 : Calculating Momentum

An 11.2kg ball moving at $39\frac{m}{s}$ strikes a 15kg ball at rest. After the collision the 11.2kg ball is moving with a velocity of $30\frac{m}{s}$ . What is the velocity of the second ball?

Possible Answers:

$6.7\frac{m}{s}$

$67.1\frac{m}{s}$

$3.4\frac{m}{s}$

$7.6\frac{m}{s}$

$5.9\frac{m}{s}$

Correct answer:

$6.7\frac{m}{s}$

Explanation:

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy.

We can use the law of conservation of momentum to equate the initial and final terms.

$m_1v_{1initial}+m_2v_{2initial}=m_1v_{1final}+m_2v_{2final}$

Plug in the given values and solve for $\small v_{2final}$ .

$(11.2kg*39\frac{m}{s})+(15kg*0\frac{m}{s})=(11.2kg*30\frac{m}{s})+(15kg*v_{2final})$

$436.8\frac{kg\cdot m}{s}+0=(336\frac{kg\cdot m}{s})+15kg( v_{2final})$

${436.8\frac{kg\cdot m}{s}}-{336\frac{kg\cdot m}{s}}=15kg( v_{2final})$

${100.8\frac{kg\cdot m}{s}}=15kg( v_{2final})$

$\frac{100.8\frac{kg\cdot m}{s}}{15kg}=v_{2final}$

$6.7\frac{m}{s}=v_{2final}$

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Example Question #18 : Calculating Momentum

A cat is playing with a 0.2kg toy mouse. He bats it with of force and is in contact with the toy for 0.1s . What is the new velocity of the mouse?

Possible Answers:

$0.5\frac{m}{s}$

$4\frac{m}{s}$

$2\frac{m}{s}$

$1\frac{m}{s}$

$0.2\frac{m}{s}$

Correct answer:

$1\frac{m}{s}$

Explanation:

Remember that momentum is equal to mass times velocity: p=mv . We can rewrite this equation in terms of force.

$mv=(kg)(\frac{m}{s})=(kg)(\frac{m}{s})*(\frac{s}{s})$

$\frac{kg*m}{s^2}*s=N*s=Ft$

Using this transformation, we can see that momentum is also equal to force times time.

$\Delta p=F\Delta t$ can also be thought of as $(p_{2}-p_{1})=F\Delta t$ .

Expand this equation to include our given values.

$(mv_{2}-mv_{1})=F\Delta t$

Since the toy starts at rest, we know the initial velocity.

$v_1=0\frac{m}{s}$

We are also given the mass, force, and time. Using these given values allows us to solve for the final velocity.

$0.2kg(v_2)-0.2kg(0\frac{m}{s})=2N(0.1s)$

$0.2kg(v_2)=2\frac{kg\cdot m}{s^2}( 0.1s)$

$0.2kg(v_2)=0.2\frac{kg\cdot m}{s}$

$v_2=\frac{0.2\frac{kg\cdot m}{s}}{0.2kg}$

$v_2=1\frac{m}{s}$

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High School Physics : Calculating Momentum

Study concepts, example questions & explanations for High School Physics

All High School Physics Resources

Example Questions

Example Question #11 : Calculating Momentum

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