A ramp 20m long slopes down 1.2m to the edge of a lake. A force of 300N is needed to pull a boat on a trailer at constant speed up the ramp when they are clear of the water. If friction is negligible, what is the combined mass of the boat and trailer.
Hints: Calculate MA of inclined plane. Then use definition of MA= Force Out/ Force in
sin A = 1.2m/20m = 0.06
A = 3.44o
Fap-Fp = m*a = m*0 = 0
300 - Fp = 0
Fp = 300 N = Force parallel to the ramp.
Fp = mg*sin A = 300 N.
m * 9.8*sin3.44 = 300
0.588m = 300
m = 510.2 kg. = Combined mass.
Wrong...
MA of inclined plane = 20m/1.2m = 16.67
&the rest idk.
In the above procedure, m*a means mass*
acceleration.
MA = 20/1.2 = 16.67=Mechanical advantage
MA = Fo/Fin = 16.67
Fo/300 = 16.67
Fo = 16.67 * 300 = 5,000 N. = Output.
m*g = 5000
m * 9.8 = 5000
m = 510.2 kg. = Combined mass.
To solve this problem, we need to use the concept of mechanical advantage (MA) of an inclined plane. The mechanical advantage is defined as the ratio of the force output to the force input.
First, let's calculate the mechanical advantage of the inclined plane using the formula MA = length of ramp / vertical height of ramp. Given that the length of the ramp is 20m and it slopes down 1.2m, the mechanical advantage can be calculated as:
MA = 20m / 1.2m
MA = 16.67
Now, we can use the definition of mechanical advantage (MA = Force Out / Force In) to find the combined mass of the boat and trailer. In this case, the force in is the force needed to pull the boat and trailer at constant speed up the ramp, which is 300N. Let's denote the force out as F_out.
Using the formula, we can rewrite the equation as:
MA = F_out / 300N
Substituting the value of mechanical advantage (MA = 16.67), we can solve for F_out:
16.67 = F_out / 300N
To find F_out, we multiply both sides of the equation by 300N:
F_out = 16.67 * 300N
F_out = 5000N
Now that we have the force output (F_out), we can equate it to the gravitational force (mg) acting on the boat and trailer to find the combined mass (m).
F_out = mg
Substituting the known value for the gravitational acceleration (g = 9.8 m/s^2), we can solve for the combined mass (m):
5000N = m * 9.8 m/s^2
Dividing both sides of the equation by 9.8 m/s^2, we get:
m = 5000N / 9.8 m/s^2
Calculating the numerical value:
m ≈ 510.2 kg
Therefore, the combined mass of the boat and trailer is approximately 510.2 kg.