A 5kg ball is attached to a 10m rope. The ball is held at a horizontal angle and allowed to fall freely with a pendulum-like motion. Assume there is no air resistance.

What is the velocity of the ball when it is at its lowest point?

Two children are playing with sleds on a snow-covered hill. Sam weighs 50kg, and his sled weighs 10kg. Sally weighs 40kg, and her sled weighs 12kg. When they arrive, they climb up the hill using boots. Halfway up the 50-meter hill, Sally slips and rolls back down to the bottom. Sam continues climbing, and eventually Sally joins him at the top. 

They then decide to sled down the hill, but disagree about who will go first. 

Scenario 1:

Sam goes down the hill first, claiming that he will reach a higher velocity.  If Sally had gone first, Sam says they could collide.

Scenario 2:

Sally goes down the hill first, claiming that she will experience lower friction and thus reach a higher velocity. If Sam had gone first, Sally says they could collide.

Scenario 3:

Unable to agree, Sam and Sally tether themselves with a rope and go down together.

If the hill is frictionless, and after both Sally and Sam reach the bottom of the hill traveling at maximum velocity, who has lost more potential energy?

Two children are playing with sleds on a snow-covered hill. Sam weighs 50kg, and his sled weighs 10kg. Sally weighs 40kg, and her sled weighs 12kg. When they arrive, they climb up the hill using boots. Halfway up the 50-meter hill, Sally slips and rolls back down to the bottom. Sam continues climbing, and eventually Sally joins him at the top. 

They then decide to sled down the hill, but disagree about who will go first. 

Scenario 1:

Sam goes down the hill first, claiming that he will reach a higher velocity. If Sally had gone first, Sam says they could collide.

Scenario 2:

Sally goes down the hill first, claiming that she will experience lower friction and thus reach a higher velocity. If Sam had gone first, Sally says they could collide.

Scenario 3:

Unable to agree, Sam and Sally tether themselves with a rope and go down together.

After reaching maximum velocity at the bottom of a frictionless hill identical to the one in the question, Sam deploys a parachute. How much energy must the parachute dissipate before Sam comes to a stop?

How much energy is required to a accelerate a  block from rest to a final speed of ?

What is the kinetic energy of a  bullet moving at ?

Two children are playing on an icy lake. Child 1 weighs 50kg, and child 2 weighs 38kg. Child 1 has a backpack that weighs 10kg, and child 2 has a backpack that weighs 5kg.

Over the course of the afternoon, they collide many times. Four collisions are described below.

Collision 1:

Child 1 starts from the top of a ramp, and after going down, reaches the lake surface while going  and subsequently slides into a stationary child 2. They remain linked together after the collision.

Collision 2:

Child 1 and child 2 are sliding in the same direction. Child 2, moving at , slides into child 1, moving at .

Collision 3:

The two children collide while traveling in opposite directions at  each.

Collision 4:

The two children push off from one another’s back, and begin moving in exactly opposite directions. Child 2 moves with a velocity of .

In collision 1, imagine that child 2 was not present on the ice. How much energy would child 1 have to dissipate to the lake surface before he came to a stop? Ignore wind resistance.

What is the kinetic energy of a 0.1kg projectile traveling at ?