A box of mass 1.95 kg slides down a frictionless ramp inclined at an angle θ= 42.9 ° at constant speed. The force exerted on the box by the ramp is how many Newtons?
To find the force exerted on the box by the ramp, we need to consider the forces acting on the box along the incline.
The gravitational force (weight) acting on the box can be expressed as:
F_gravity = m * g
where m is the mass (1.95 kg) and g is the acceleration due to gravity (9.8 m/s^2).
The force exerted by the ramp along the incline can be decomposed into two components: the gravitational force and the normal force (perpendicular to the incline).
The normal force can be calculated using the equation:
F_normal = m * g * cos(θ)
where θ is the angle of the incline (42.9 degrees).
Since the box is sliding down the ramp at a constant speed, the net force acting on the box is zero. Therefore, the force exerted on the box by the ramp is equal in magnitude but opposite in direction to the component of the gravitational force along the incline.
The force exerted on the box by the ramp is given by:
F_ramp = - F_gravity * sin(θ)
Substituting the values into the equations:
F_gravity = (1.95 kg) * (9.8 m/s^2) ≈ 19.11 N
F_normal = (1.95 kg) * (9.8 m/s^2) * cos(42.9°) ≈ 14.30 N
F_ramp = - (19.11 N) * sin(42.9°) ≈ -12.99 N
So, the force exerted on the box by the ramp is approximately 12.99 Newtons.
To determine the force exerted on the box by the ramp, we need to consider the forces acting on the box. Since the box is sliding down the frictionless ramp at a constant speed, we know that the sum of the forces in the direction parallel to the ramp (down the incline) must be zero.
The forces acting on the box in the direction down the incline are:
1. The gravitational force pulling the box downwards (mg), where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. The force exerted on the box by the ramp (Framp), which we need to find.
Since the box is moving at a constant speed, the sum of these two forces (Framp and mg) must be zero. Therefore, we have:
Framp + mg = 0
Rearranging this equation, we can isolate the force exerted on the box by the ramp:
Framp = -mg
Substituting the given values:
m = 1.95 kg
g ≈ 9.8 m/s^2
Framp = -(1.95 kg) * (9.8 m/s^2)
Calculating the value:
Framp ≈ -19.11 N
Note: The negative sign indicates that the force exerted by the ramp acts in the opposite direction to the force of gravity.