A spring is suspended on the ceiling of a truck, find acceleration?

In summary, a massless spring with a spring constant of 500 N/m is suspended from a hook on the ceiling of a moving cargo truck. A toy with a mass of 1.1 kg is hung from the free end of the spring, causing it to extend by 5.0 cm. The task is to find the acceleration of the truck. To solve this problem, a free body diagram must be drawn taking into account the forces on the spring, including the spring force and the net force.
  • #1
greenglasses
23
0

Homework Statement



A massless spring with a spring constant k = 500 N/m is suspended from a hook on the ceiling of a cargo truck moving in a straight line (horizontally) on the highway. A child reaches over from her seat and suspends a 1.1 kg toy on the free end of the spring. The child notices that the spring is now 5.0 cm longer than when it was hanging freely. Find the acceleration for the truck.

Homework Equations



Fk = -kx
Fnet = ma

The Attempt at a Solution



I honestly have no clue what to do since the spring force is in the vertical direction but the truck is accelerating horizontally. Would appreciate any pointers in the right direction.
 
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  • #2
greenglasses said:

The Attempt at a Solution



I honestly have no clue what to do since the spring force is in the vertical direction but the truck is accelerating horizontally. Would appreciate any pointers in the right direction.

Draw a free body diagram. The weighted spring will not remain vertical when the truck is accelerating. The greater the acceleration, the greater the spring extends and the greater the springs angle wrt vertical becomes.
 

1. How does the acceleration of the truck affect the motion of the spring?

The acceleration of the truck will affect the motion of the spring because the spring is attached to the ceiling of the truck. As the truck accelerates, the spring will experience a force in the opposite direction, causing it to stretch or compress depending on the direction of acceleration.

2. How can we calculate the acceleration of the truck using the spring's motion?

In order to calculate the acceleration of the truck, we can use the equation F=ma, where F is the force exerted on the spring, m is the mass of the spring, and a is the acceleration of the truck. By measuring the displacement of the spring and knowing its spring constant, we can solve for the acceleration.

3. What factors can affect the accuracy of the acceleration calculation using the spring?

There are several factors that can affect the accuracy of the acceleration calculation using the spring. These include friction between the spring and the ceiling of the truck, air resistance, and the elasticity of the spring. It is important to minimize these factors to obtain a more accurate calculation.

4. How does the mass of the spring affect its motion in the truck?

The mass of the spring will affect its motion in the truck because it will determine the amount of force required to stretch or compress the spring. A heavier spring will require more force to achieve the same displacement as a lighter spring. This can also affect the acceleration calculation, as the mass of the spring is a factor in the equation F=ma.

5. What other real-life examples can be used to demonstrate the concept of acceleration using a spring?

One real-life example is a car's suspension system. The car's body is suspended on springs, and as the car accelerates, the springs experience a force in the opposite direction, similar to the spring in the truck. Another example is a pogo stick, where the spring compresses and stretches as the person jumps up and down, demonstrating the concept of acceleration due to the force of gravity.

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