Solving Physics Problems: Sleds, Trucks, Bullets & Cars

[explorer]

1. A 16-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 24 N. Starting from rest, the sled attains a speed of 2 m/s in 8 m. Find the coefficient of kinetic friction between the runners of the sled and the snow.

2. A dump truck of 2500 kg is being filled with sand. The sand falls straight downward from rest from a height of 2 m above the truck bed, and the mass of sand that hits the truck per second is 55 kg/s. The truck is parked on the platform of a weight scale. By how much does the scale reading exceed the weight of the truck and sand?

3. An 8-g bullet is fired into a 250-g block that is initially at rest at the edge of a smooth table of height 1 m, as shown in the figure. The bullet remains in the block, and after the impact the block lands 2 m from the bottom of the table. Determine the initial speed of the bullet.


4. A 1200-kg car traveling initially with a speed of 25 m/s due east crashes into the rear end of a 9000-kg truck moving in the same direction at 20 m/s. The velocity of the car right after the collision is 18 m/s to the east. How much mechanical energy is lost in the collision?

Thanks a lot.

 

[HallsofIvy]

Help you- yes. Do them for you- no. Do what you can and show us what you have tried. That will help us understand what kind of help you need.

 

[M98Ranger]

1. To solve this problem, we can use the equation F=ma, where F is the net force, m is the mass, and a is the acceleration. In this case, the net force is the horizontal force of 24 N pulling the sled, and the mass is 16 kg. We also know that the sled starts from rest and attains a speed of 2 m/s in 8 m, so we can use the equation v^2 = u^2 + 2as to find the acceleration. Plugging in the values, we get a = 0.5 m/s^2. Now, we can use the equation Ff = μmg, where Ff is the force of kinetic friction, μ is the coefficient of kinetic friction, m is the mass, and g is the acceleration due to gravity. Solving for μ, we get μ = Ff/mg = ma/mg = a/g = 0.5/9.8 = 0.051. Therefore, the coefficient of kinetic friction between the runners of the sled and the snow is 0.051.

2. To solve this problem, we can use the equation F=ma, where F is the net force, m is the mass, and a is the acceleration. In this case, the net force is the weight of the sand falling, and the mass is the rate of sand falling per second (55 kg/s). We also know that the sand falls from a height of 2 m, so we can use the equation PE = mgh to find the potential energy of the sand. This potential energy is then converted into kinetic energy as the sand falls, so we can use the equation KE = 1/2mv^2 to find the velocity of the sand when it hits the truck. Plugging in the values, we get v = √(2gh) = √(2*9.8*2) = 6.26 m/s. Now, we can use the equation F=ma again to find the force of the sand hitting the truck, which is also the force that causes the scale to read higher. Solving for F, we get F = ma = 55*6.26 = 343.3 N. Therefore, the scale reading will exceed the weight of the truck and sand by 343.3 N.

3. To solve this problem, we can use the principle of conservation