a hockey player pushes a puck across the ice with his stick. assuming the puck (m=50 g) starts from rest and the player applies a force of 100 N over a distance of 10 cm, how fast is the puck moving after it leaves his stick?
1/2 mv^2= force*distance
solve for v.
To find the speed of the puck after it leaves the player's stick, we can utilize Newton's second law of motion and apply the concept of work and energy.
Step 1: Convert the given distance into meters.
The distance is given as 10 cm. One meter is equal to 100 centimeters, so the distance in meters is 10 cm / 100 = 0.1 m.
Step 2: Convert the mass of the puck into kilograms.
The mass is given as 50 grams. One kilogram is equal to 1000 grams, so the mass of the puck in kilograms is 50 g / 1000 = 0.05 kg.
Step 3: Calculate the work done on the puck.
The work done on an object is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force applied is 100 N, and the distance is 0.1 m. So the work done on the puck is 100 N * 0.1 m = 10 J (joules).
Step 4: Apply the work-energy principle.
According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the puck is 10 J, and the initial kinetic energy is zero (since the puck starts from rest).
Step 5: Calculate the final kinetic energy of the puck.
Since the initial kinetic energy is zero, the final kinetic energy is equal to the work done on the puck. Therefore, the final kinetic energy is also 10 J.
Step 6: Use the equation for kinetic energy to find the final velocity of the puck.
The equation for kinetic energy is given by KE = 1/2 * mass * velocity^2. We already know that the final kinetic energy is 10 J, and the mass of the puck is 0.05 kg. Plugging these values into the equation, we have 10 J = 1/2 * 0.05 kg * velocity^2.
Step 7: Solve for the velocity.
Rearranging the equation from step 6, we have velocity^2 = (2 * final kinetic energy) / mass. Plugging in the given values, we get velocity^2 = (2 * 10 J) / 0.05 kg.
Simplifying further, velocity^2 = 400 m^2/s^2.
Finally, taking the square root of both sides, we find velocity = sqrt(400) m/s = 20 m/s.
Therefore, the puck is moving at a speed of 20 m/s after it leaves the player's stick.