Calculate Paul's Speed with Work and Energy: Friction & Tension on a Mat

[vtx7]

Susan's 13.0 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30 degrees above the floor. The tension is a constant 30.0 N and the coefficient of friction is 0.180.

Use work and energy to find Paul's speed after being pulled 2.60 m

So far I found the forces acting on the system to be:

Y:
127.5N down due to gravity
15N up due to tension
112.5N normal force
X:
25.98 due to tension
-20.25 due to friction

So I get a net force of 5.73N which I thought if I divided by the mass of 13kg it would give me that speed, but that is wrong. I am stuck here guys.

Thanks in advance for the help

 

[Phlogistonian]

Force divided by mass is acceleration.

The instructions say to use work and energy. Now that you have the net force, use that to calculate the work. And then use the change in kinetic energy to calculate the speed.

 

[Moetasim]

Based on the given information, we can use the work-energy theorem to calculate Paul's speed after being pulled 2.60 m. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on Paul will come from the tension force and the friction force.

First, we need to calculate the work done by the tension force. Since the rope is angled 30 degrees above the floor, we can use trigonometry to find the component of the tension force in the direction of motion. The component of the tension force in the x-direction is given by T*cos(30) = 30*cos(30) = 25.98 N. The work done by this force is then W = F*d*cos(30) = 25.98*2.60*cos(30) = 33.77 J.

Next, we need to calculate the work done by the friction force. The work done by friction is given by W = μ*F*d, where μ is the coefficient of friction, F is the normal force, and d is the distance. In this case, the normal force is equal to the weight of Paul, which is 127.5 N. Therefore, the work done by friction is W = 0.180*127.5*2.60 = 58.05 J.

Now, we can use the work-energy theorem to find Paul's speed. The total work done on Paul is equal to the change in his kinetic energy, which can be expressed as:

W = ΔKE = (1/2)*m*v^2 - (1/2)*m*vo^2

Where m is Paul's mass, v is his final speed, and vo is his initial speed (which we assume to be 0). Rearranging this equation, we get:

v = √(2*W/m)

Substituting the values we calculated for W and m, we get:

v = √(2*(33.77 - 58.05)/13) = √(-49.56/13) = -2.24 m/s

Note that the negative sign indicates that Paul's speed is in the opposite direction of the applied force. This means that Paul is slowing down rather than speeding up. This could be due to the presence of friction, which is acting in the opposite direction of motion. If we