A patient of mass 75kg sits in a wheelchair of mass 30kg. What is the force needed to push both up a 30 degree slope? If the carer stops on the 30 degree slope and applies the brake, what is the magnitude and direction of the frictional force preventing the wheelchair from rolling back down?
on the slope, there are three forces
Force pushing- force down the plane-frictional force= ma assuming constant speed, (a=0) then
force pushing= mgSin30+friction. If you assume rolling friction is zero, you have it.
Now, if stopped
mgsin30=frictional force
this seems too easy.
To calculate the force needed to push both the patient and the wheelchair up a 30-degree slope, we need to consider the gravitational force and the component of the force parallel to the slope that opposes it.
1. Gravitational Force:
The gravitational force acting on an object is given by the equation Fg = mg, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2 near the Earth's surface). In this case, the total mass is the sum of the patient's mass and the wheelchair's mass: m_total = m_patient + m_wheelchair. Let's calculate the gravitational force acting on both:
m_patient = 75 kg (mass of patient)
m_wheelchair = 30 kg (mass of wheelchair)
Fg = mg_patient + mg_wheelchair
= (75 kg)(9.8 m/s^2) + (30 kg)(9.8 m/s^2)
= 735 N + 294 N
= 1029 N
So, the gravitational force acting on both the patient and the wheelchair is 1029 N.
2. Component of the Force Parallel to the Slope:
To find the force needed to push both up the slope, we need to determine the component of the gravitational force parallel to the slope. This component can be calculated using the equation F_parallel = Fg * sin(theta), where theta is the angle of the slope (30 degrees in this case).
F_parallel = Fg * sin(theta)
= 1029 N * sin(30 degrees)
= 1029 N * 0.5
= 514.5 N
So, the force needed to push both the patient and the wheelchair up the 30-degree slope is approximately 514.5 N.
Now, let's move on to the second part of the question:
When the carer stops on the 30-degree slope and applies the brake, the wheelchair might try to roll back down the slope due to the gravitational force acting on it. However, the frictional force between the wheelchair's wheels and the slope acts in the opposite direction, preventing it from rolling back. The magnitude of the frictional force can be calculated using the equation F_friction = μ * N, where μ is the coefficient of friction and N is the normal force, which is equal to the gravitational force acting perpendicular to the slope.
In this case, the frictional force is preventing the wheelchair from rolling back, so it acts in the opposite direction to the component of the gravitational force parallel to the slope. Therefore, the magnitude of the frictional force is equal to the force needed to push both up the slope, which we found earlier to be 514.5 N.
The direction of the frictional force is opposing the tendency of the wheelchair to slide down the slope, which means it acts uphill. So, the direction of the frictional force is uphill.