a trolley of mass 40kg us pushed up a hill of height 10m at an angle of 20 degree. calculate the force required to reach this height. how do i complete this question?
m*g = 40kg * 9.8N/kg = 392 N. = Wt. of
trolley.
Fp = 392*sin20 = 134.1 N. = Force parallel to the hill.
F-Fp = m*a
F-134.1 = m*0 = 0
F = 134.1 N.
To calculate the force required to push the trolley up the hill, we need to consider the gravitational force, the vertical component of the force applied, and the force of friction. Here are the steps to complete this question:
Step 1: Calculate the gravitational force acting on the trolley.
The gravitational force can be calculated using the formula: F_gravity = mass * acceleration due to gravity. In this case, the mass is 40 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, F_gravity = 40 kg * 9.8 m/s^2.
Step 2: Calculate the vertical component of the force applied.
The angle of the hill is given as 20 degrees. To determine the vertical component of the force applied, we need to use trigonometry. The vertical component is given by: Force_vertical = force_applied * sin(angle). In this case, the angle is 20 degrees.
Step 3: Determine the force of friction.
The force of friction opposes the motion of the trolley up the hill. If the trolley is not slipping or skidding, we can assume that the force of friction is equal to the vertical component of the force applied. Therefore, Force_friction = Force_vertical determined in Step 2.
Step 4: Calculate the total force required.
The total force required is the sum of the gravitational force and the force of friction. Therefore, Force_total = F_gravity + Force_friction determined in Step 3.
By following these steps and plugging in the values given, you can calculate the force required to reach the height of 10 m up the hill.