A 1 kg block of wood is moving with a velocity of 10 ms-1

Question

1. A 1 kg block of wood is moving with a velocity of 10 m/s^-1 on top of a table. The coefficient of kinetic friction between the block of wood and the table is 0.1. The block of wood is a cube with sides of 12 cm.

a) How far does the block move before coming to a stop?

b) If momentum id conserved, where did the momentum of the block go?

c) The block slows down because of the frictional force between the block and the block. However, if the frictional force acts at the bottom of the block and the blocks center of mass is in the center of the block then there must be a torque acting on the block. Calculate this torque. Why doesn't this torque cause the block to rotate?

2. In 2286, Admiral Kirk and his crew were forced to use the sling shot effect in a stolen Klingon Bird-of-Prey to travel back in time to the late 20th century to retrieve two humpback whales. The stolen Klingon Bird-of-Prey traveled towards the sun at a velocity of v, while the sun was moving towards them at a velocity of u, then traveled around the sun (using the sun's gravitational field) such that the stolen Klingon Bird-of-Prey was now moving in the opposite direction from whence it started, with a new velocity, v_new. Find vnew in terms of u and v, assuming the mass of the sun is much larger than the mass of the spaceship.

3. Consider holding a carton of milk in your hand, as shown in the image. The force of the bicep muscle acts at an angle of 15o to the vertical, while the weight of the arm and the milk both act downwards. The distance from the elbow to where the bicep muscle is attached via the the distal bicep tendons to the radius and ulna bones is 5 cm. The distance from the elbow to the center of mass of the forearm is 16.5 cm and the distance from the elbow to the hand, holding the milk, is 35 cm. The forearm has a mass of 4 kg and the milk carton a mass of 2 kg.

a) Assuming the forearm is kept perfectly horizontal, find the tension in the bicep muscle.

b) As a function of the angle of the forearm with respect to the horizontal direction (as the forearm is lowered) calculate the tension in the bicep muscle.

c) Include a plot of tension in the bicep as a function of the angle of the forearm relative to the horizontal (don't forget to label axis).