You push a 67 kg box across a floor where the coefficient of kinetic friction is uk = .55. The force you exert is horizontal. (a) How much power is needed to push the box at a speed of .50 m/s? (b) How much work do you do if you push the box for 35 s?

*please list the steps to work out this question.

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To find the power needed to push the box at a speed of 0.50 m/s and the work done if you push the box for 35 seconds, you'll need to follow these steps:

(a) Calculating Power:
Step 1: Determine the force of kinetic friction acting on the box.
- The force of kinetic friction (Fk) can be calculated using the formula: Fk = uk * Fn, where uk is the coefficient of kinetic friction and Fn is the normal force.
- The normal force (Fn) can be calculated as the weight of the box, which is given by the formula: Fn = m * g, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s²).
- Substitute the values: m = 67 kg, uk = 0.55, and g = 9.8 m/s² to find Fk.

Step 2: Calculate the net force acting on the box.
- The net force (Fnet) can be calculated as the force applied minus the force of kinetic friction. Since the box is moving at a constant speed, the net force is zero.
- Using the equation: Fnet = Fapp - Fk, set Fnet equal to zero and solve for Fapp (the applied force).

Step 3: Calculate the work done.
- The work done (W) can be calculated using the formula: W = Fapp * d, where Fapp is the applied force and d is the distance over which the force is applied.
- Since the box is moving at a constant speed, the work done is equal to the force applied multiplied by the distance traveled.
- Substitute the values: Fapp = calculated in Step 2 (in Newtons), and d is not provided in the question, so it needs to be specified or assumed.

Step 4: Calculate the power.
- Power (P) is defined as the rate at which work is done, so it can be calculated as the work done divided by the time taken.
- Substitute the values: W (calculated in Step 3) and the given time of 35 s to find P.

(b) Calculating Work:
Follow Steps 1 and 2 from part (a) to calculate Fapp (applied force).

Step 3: Calculate the work done (W) using the formula: W = Fapp * d, where Fapp is the applied force and d is the distance.
- You know the time (35 s) and the speed (0.50 m/s), so you can calculate the distance (d) using the formula: d = speed * time.

Note: Make sure to convert units if necessary and use the appropriate equations, keeping track of the variables provided in the question.

NOOOOOOB

power= force*velocity

power= .55*67*g*.5 watts

work= power*time

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