Question

Why is it difficult to move a bike with its brake on?

Answer 1

The brake is used in a vehicle to control its speed. The brake is also used to stop the vehicle. The usage of brakes is related to the frictional force. With the brakes on, it's difficult to roll the wheel of the bike. Three types of friction related to solid substances exist, static friction, sliding friction, and rolling friction.

Complete step-by-step solution:
A brake of a bike reduces the speed of the bike or prevents it from moving.
All brakes are designed to give a friction-creating brake pad against a braking surface on the moving wheel of the vehicles by way of a hand-operated lever. with the increase in pressure at the brake lever, the force due to the friction is increased. This works in combination with a tire's grip to slow the bike down.
Brakes are used for no rolling of wheels. Hence with brakes on, to displace a bike seems like trying to move a body having no wheels. In this case, the sliding friction is larger than the rolling friction, so it is difficult to move a bike with the brakes on.

Note: The force due to the friction works in the forward direction on the rear wheel. It works in the backward direction on the front wheel. The amount of frictional force acting on the rear wheel can be greater than, equal to, or less than that on the front wheel.
The force on the rear wheel is greater than that on the front wheel during the acceleration of the bicycle.
These two are the same when the bicycle moves at a constant speed.
The force on the rear wheel is less than that on the front wheel during the retardation of the bicycle.