A body of mass 7.5kg is to be pulled up along a plane which is inclined at 30degree to the horizontal. If the efficiency of the plane is 75 %, what is the minimum force required to pull the body up the plane?
To find the minimum force required to pull the body up the plane, we need to consider the force of gravity and the efficiency of the plane.
1. First, let's find the force of gravity acting on the body. The force of gravity (weight) can be calculated using the formula:
Weight = mass * gravity
Given that the mass of the body is 7.5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 7.5 kg * 9.8 m/s^2 = 73.5 N
2. Next, we need to find the force required to move the body up the plane. The force required can be calculated using the formula:
Force required = Weight / (sinθ)
where θ is the angle of inclination, which is given as 30 degrees.
Using this formula, we can calculate the force required:
Force required = 73.5 N / sin(30 degrees) ≈ 147 N
3. Finally, we need to calculate the minimum force required taking into account the efficiency of the plane. The minimum force required can be calculated using the formula:
Minimum force = Force required / efficiency
Given that the efficiency of the plane is 75%, we can calculate the minimum force required:
Minimum force = 147 N / 0.75 ≈ 196 N
Therefore, the minimum force required to pull the body up the plane is approximately 196 Newtons.
To find the minimum force required to pull the body up the incline, we need to understand the concepts of force, work, and efficiency.
1. Start by calculating the gravitational force acting on the body. We can use the formula F = mg, where m is the mass of the body (7.5 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F = (7.5 kg) x (9.8 m/s^2)
F = 73.5 N
2. Now, determine the work done by the gravitational force when the body is raised to the height of the incline. The work done is given by the formula W = Fd, where W is the work done, F is the force, and d is the displacement.
Since the displacement is along an incline, we need to consider the effective displacement, which is the height of the incline multiplied by the sine of the angle.
d = h x sin(angle)
d = unknown x sin(30°)
Since we don't have the height (h), we'll substitute it as "unknown."
3. The work done by the gravitational force is equal to the work done by the applied force, considering the efficiency of the incline. The work done by the applied force is given by the formula W = F_applied * d. Thus, we can set up the following equation:
F_applied * d = 0.75 * F_gravitational * d
Now, we can substitute the known values:
F_applied * unknown x sin(30°) = 0.75 * (73.5 N) * unknown x sin(30°)
4. Next, we can rearrange the equation to solve for F_applied:
F_applied = (0.75 * (73.5 N) * unknown x sin(30°)) / (unknown x sin(30°))
The unknowns (height) cancel out, and the value of sin(30°) is 0.5.
F_applied = (0.75 * (73.5 N) * 0.5) / 0.5
F_applied = 36.75 N
Therefore, the minimum force required to pull the body up the incline is approximately 36.75 Newtons.
F = mg sin30/.75
Although I've never heard of efficiency of an inclined plane.