A 21.1 g ball of clay is thrown horizontally at + 38.7 m/s toward a 1.2 kg block sitting at rest on a frictionless surface. The clay hits and sticks to the block.

A. What is the speed of the block and clay right after the collision?


m/s
B. Use the block's initial and final speeds to calculate the impulse the clay exerts on the block
kg m/s
C. Use the clay's initial and final speeds to calculate the impulse the block exerts on the clay.
kg m/s

To solve this problem, we'll use the principles of conservation of momentum and the equation for impulse.

A. To find the speed of the block and clay right after the collision, we need to find the total momentum of the system before and after the collision. The momentum of an object is given by the product of its mass and velocity.

Before the collision, the ball of clay has a momentum of (mass of clay) × (velocity of clay) = (21.1 g) × (38.7 m/s) = 816.57 g·m/s.

Since the block is initially at rest, its momentum is zero.

The total momentum before the collision is therefore 816.57 g·m/s.

After the collision, the ball of clay and the block stick together, so they move as one combined object. Let's call their final velocity v.

The total momentum after the collision is (mass of clay + mass of block) × v. Since the clay sticks to the block, their masses add up: (21.1 g + 1.2 kg) × v = 1210.0 g·m/s.

To find v, let's convert the masses and solve for v:

(0.0211 kg + 1.2 kg) × v = 1.210 kg·m/s
(1.2211 kg) × v = 1.210 kg·m/s
v = 1.210 kg·m/s / 1.2211 kg
v ≈ 0.9917 m/s

So the speed of the block and clay right after the collision is approximately 0.9917 m/s.

B. To calculate the impulse the clay exerts on the block, we can use the equation for impulse: impulse = change in momentum.

The initial momentum of the block is zero, and its final momentum can be calculated using its mass and velocity after the collision. The change in momentum is simply the final momentum of the block.

Final momentum of the block = (mass of block) × (final velocity of block)
= (1.2 kg) × (0.9917 m/s)
= 1.1900 kg·m/s.

The impulse the clay exerts on the block is the change in momentum, so it's also 1.1900 kg·m/s.

C. Similarly, to calculate the impulse the block exerts on the clay, we can use the equation for impulse.

The initial momentum of the clay is given by its mass and velocity before the collision. The final momentum can be calculated using its mass and velocity after the collision, which is the same as the final velocity of the combined block and clay.

Initial momentum of the clay = (mass of clay) × (initial velocity of clay)
= (21.1 g) × (38.7 m/s)
= 816.57 g·m/s.

Final momentum of the clay = (mass of clay) × (final velocity of the block and clay)
= (21.1 g) × (0.9917 m/s)
= 20.8937 g·m/s.

The change in momentum is the final momentum of the clay minus the initial momentum:

Impulse the block exerts on the clay = Final momentum of the clay - Initial momentum of the clay
= 20.8937 g·m/s - 816.57 g·m/s
≈ -795.6763 g·m/s.

However, since the block exerts a force on the clay in the opposite direction, we take the magnitude of the impulse. So the impulse the block exerts on the clay is approximately 795.6763 g·m/s.