A 25kg mass is on a level, rough surface where the force of friction is a constant 15 N. A horizontal applied force of 65 N acts on the mass. The mass is initially at rest.
a) what speed does the mass have after 4.0 seconds?
b) what speed does the mass have after being moved 2.0m?
force pulled-friction= ma
start with that, solve for a.
Fnet=65-15=0?
50 is the answer?
I got finally got letter a but im stuck at b now :(
if you have a...
Vf^2=Vi^2+2ad
Vi is zero, you know a, and d. solve for Vf
To answer these questions, we will need to apply Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration (F = ma). We'll also need to consider the equation for the force of friction, which is given by the product of the coefficient of friction (μ) and the normal force (N). In this case, since the surface is level, the normal force N is equal to the weight of the object.
Let's break down the problem into parts:
a) To find the speed of the mass after 4.0 seconds, we need to calculate the acceleration first.
1. Determine the net force: The net force acting on the mass is the difference between the applied force (65 N) and the force of friction (15 N). So, the net force is 65 N - 15 N = 50 N.
2. Calculate acceleration: Use Newton's second law to find the acceleration. Rearranging the equation, we have a = F/m. Substituting the values, we get a = 50 N / 25 kg = 2 m/s^2.
3. Calculate speed: Now, we can calculate the speed of the mass after 4.0 seconds using the equation v = u + at, where u is the initial velocity (which is 0 m/s) and t is the time (4.0 seconds). Substitute the values: v = 0 + 2 m/s^2 * 4.0 s = 8.0 m/s.
Therefore, the speed of the mass after 4.0 seconds is 8.0 m/s.
b) To find the speed of the mass after being moved 2.0 m, we'll first calculate the work done on the mass, and then use the work-energy principle to find the speed.
1. Calculate work done: The work done on an object is given by the equation W = Fd, where F is the applied force and d is the distance. Substitute the values: W = 65 N * 2.0 m = 130 J.
2. Apply the work-energy principle: The work done on an object is equal to its change in kinetic energy. In this case, the work done is equal to the change in kinetic energy. So, we have W = ΔKE.
3. Calculate the change in kinetic energy: The change in kinetic energy is equal to the final kinetic energy (KE) minus the initial kinetic energy. Since the mass was initially at rest, the initial kinetic energy is 0. Therefore, we have ΔKE = KE - 0 = KE.
4. Convert work into kinetic energy: Using ΔKE = W, we can substitute the values: KE = 130 J.
5. Calculate speed: The kinetic energy (KE) is given by the equation KE = (1/2)mv^2, where m is the mass and v is the velocity. Rearrange the equation to solve for v: v = √(2KE/m). Substitute the values: v = √(2 * 130 J / 25 kg) ≈ 5.08 m/s.
Therefore, the speed of the mass after being moved 2.0 m is approximately 5.08 m/s.