A horse pulls on a crate with a 1,000 N force, causing it to move at constant velocity. What is the acceleration of the cart? A 44-kg child steps onto a scale. What is the magnitude of the force that the scale exerts on the child
These are two different questions
(1) Constant velocity means zero acceleration.
(2) Weight = M*g = 44*9.8 Newtons
It is the same force that the child exerts on the scale.
Well, if the horse is pulling on the crate with a force of 1,000 N and the crate is moving at a constant velocity, that means there is no net acceleration. So, the acceleration of the cart is a big fat zero. It's just having a lazy day, I suppose.
As for the 44-kg child stepping onto a scale, the magnitude of the force that the scale exerts on the child is the same as the magnitude of the force that the child exerts on the scale. So, let's just say the scale has to deal with the weight of carrying around a 44-kg bundle of joy. It's like a workout for the scale, but hopefully it won't break a sweat.
To determine the acceleration of the cart, we need to consider the forces acting on it. The only force acting on the cart is the force applied by the horse, which is 1,000 N. Since the cart is moving at a constant velocity, we can conclude that the net force acting on the cart is zero.
Newton's second law states that the net force on an object is equal to its mass multiplied by its acceleration (F = m * a). Since the net force is zero, the acceleration of the cart is also zero.
Now, let's move on to the second question. When a 44-kg child steps onto a scale, the scale exerts a force on the child equal to the weight of the child.
The weight of an object is given by the formula W = m * g, where m is the mass of the object and g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on the surface of the Earth.
To find the magnitude of the force that the scale exerts on the child, we need to calculate the weight of the child: W = 44 kg * 9.8 m/s^2 = 431.2 N.
Therefore, the magnitude of the force that the scale exerts on the child is 431.2 N.
To find the acceleration of the crate, we need to know its mass. The equation that relates force, mass, and acceleration is F = m*a, where F is the force, m is the mass, and a is the acceleration. In this case, the horse exerts a force of 1,000 N on the crate.
If the crate is moving at a constant velocity, it means that the net force acting on it is zero. This means that the force exerted by the horse is balanced by an equal and opposite frictional force. Therefore, the frictional force must also be 1,000 N in the opposite direction.
Since the net force is zero, the acceleration is also zero. This means that the crate is not accelerating and is moving at a constant velocity.
To find the magnitude of the force that the scale exerts on the child, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. The equation is F = m*a.
In this case, the mass of the child is given as 44 kg. Since the child is standing on the scale and not moving vertically, we can assume that the acceleration is zero. Therefore, the net force acting on the child is also zero.
The force that the scale exerts on the child is equal in magnitude but opposite in direction to the force exerted by the child on the scale. Therefore, the magnitude of the force that the scale exerts on the child is also zero.