A man pushes a packing case of total mass 40kg across a floor at a constant speed of 0.5m/s by exerting a horizontal force of 100N
what is the resultant force on the case
how big was the force of friction acting on the case
how much work was done in 3s
what is the Ek
into what forms of enrgy is the work done converted
what effective power does the man produce
To calculate the resultant force on the case, we can use Newton's second law, which states that the resultant force is equal to mass multiplied by acceleration. Since the case is moving at a constant speed, the acceleration is zero. Therefore, the resultant force is also zero.
The force of friction can be calculated using the formula F_friction = μ × F_normal, where μ is the coefficient of friction and F_normal is the normal force. Since the case is on a horizontal surface, the normal force is equal to the weight of the case, which can be calculated as mass multiplied by gravity. Assuming a coefficient of friction of 0.2 and a gravitational acceleration of 9.8 m/s^2, the force of friction can be calculated as follows:
F_friction = 0.2 × (mass × gravity)
F_friction = 0.2 × (40 kg × 9.8 m/s^2)
F_friction = 78.4 N
The work done can be calculated using the formula W = F × d, where W is the work done, F is the force exerted, and d is the distance. In this case, the force exerted is 100N and the distance can be calculated as the product of speed and time:
distance = speed × time
distance = 0.5 m/s × 3 s
distance = 1.5 m
Therefore, the work done can be calculated as follows:
W = 100 N × 1.5 m
W = 150 J
The kinetic energy (Ek) can be calculated using the formula Ek = 0.5 × mass × velocity^2. In this case:
Ek = 0.5 × 40 kg × (0.5 m/s)^2
Ek = 5 J
The work done is converted into kinetic energy and thermal energy. The kinetic energy represents the energy of the moving object (the case), while the thermal energy represents the energy dissipated as heat due to friction.
The effective power produced by the man can be calculated using the formula P = W / t, where P is the power, W is the work done, and t is the time. In this case:
P = 150 J / 3 s
P = 50 W
Therefore, the man produces an effective power of 50 watts.
To answer these questions, we'll need to use some basic physics principles and formulas. Let's break down each question and explain how to find the answer:
1. Resultant force on the case:
The resultant force is the sum of all forces acting on an object. In this case, we have the horizontal force applied by the man and the force of friction opposing the motion. Since the case is moving at a constant speed, we know that the net force is zero (because the net force on an object at constant velocity is zero). Hence, the resultant force on the case is zero.
2. Force of friction:
Since the resultant force is zero and the applied force by the man is 100N, the force of friction must be equal and opposite to the applied force. Therefore, the force of friction on the case is also 100N.
3. Work done in 3 seconds:
Work is calculated using the formula: work = force × distance. In this case, we have the force of friction opposing the motion, and the distance covered by the case can be calculated using the formula: distance = speed × time. The distance covered by the case in 3 seconds is 0.5 m/s × 3 s = 1.5 meters. Therefore, the work done in 3 seconds is work = force of friction × distance = 100N × 1.5m = 150 Joules.
4. Kinetic energy (Ek):
Kinetic energy is the energy possessed by an object due to its motion and is given by the formula: Ek = 0.5 × mass × speed^2. In this case, the mass of the case is given as 40 kg and the speed is given as 0.5 m/s. Plugging these values into the formula, we get: Ek = 0.5 × 40 kg × (0.5 m/s)^2 = 5 Joules.
5. Forms of energy conversion:
When work is done on an object, energy is converted from one form to another. In this case, the work done by the man is converted into kinetic energy of the case. So the work done is converted into kinetic energy.
6. Effective power produced by the man:
Power is the rate at which work is done or energy is transferred. The formula to calculate power is: power = work/time. We already know that the work done in 3 seconds is 150 Joules. Dividing this by the time of 3 seconds, we get: power = 150 Joules / 3 seconds = 50 Watts. Therefore, the effective power produced by the man is 50 Watts.