If a boulder of 9.7 tons is placed on a 70 degree incline, how much extra force would be needed to push the boulder up if the incline increases up by 5 degrees?
To find the extra force needed to push the boulder up the incline, we can break down the problem into two components: the force due to gravity and the force due to the incline.
1. Force due to gravity:
The force due to gravity can be calculated using the formula F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2). The mass of the boulder can be converted from tons to kilograms by multiplying by 1000 (1 ton = 1000 kg). So, the mass of the boulder is 9.7 tons * 1000 kg/ton = 9700 kg. Therefore, the force due to gravity is F_gravity = 9700 kg * 9.8 m/s^2.
2. Force due to the incline:
The force due to the incline can be calculated using the formula F = m * g * sin(theta), where theta is the angle of the incline. Initially, the angle of the incline is 70 degrees. The force due to the incline can be found by multiplying the mass and the acceleration due to gravity by the sine of the angle. So, F_incline_initial = 9700 kg * 9.8 m/s^2 * sin(70 degrees).
To determine the extra force required when the incline increases by 5 degrees, we need to calculate the force due to the incline at the new angle. The new angle is 70 + 5 = 75 degrees. So, F_incline_new = 9700 kg * 9.8 m/s^2 * sin(75 degrees).
Finally, we can find the extra force needed to push the boulder up by subtracting the initial force due to the incline from the new force due to the incline. The extra force required is: F_extra = F_incline_new - F_incline_initial.