A light spring having a force constant of 110  is used to pull a 15.0  sled on a horizontal frictionless ice rink. The sled has an acceleration of 1.60 ?

[2/27/12 9:41:56 PM] Matt Yeager: By how much does the spring stretch if it pulls on the sled at 29.0 above the horizontal?

There are no units here, it is impossible to work without units. On the second question, one has to know the spring constant.

To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is proportional to its displacement from its equilibrium position.

First, let's determine the force exerted by the spring on the sled. We can use the formula:

F = k * x

where F is the force, k is the force constant of the spring, and x is the displacement of the spring from its equilibrium position. In this case, the force constant is 110 N.

The force exerted by the spring can also be calculated using the horizontal and vertical components. The vertical component is given as 29.0° above the horizontal. Therefore, the vertical component of the force, Fy, is given by:

Fy = F * sin(θ)

where θ is the angle of 29.0°. The horizontal component of the force, Fx, is given by:

Fx = F * cos(θ)

The sled has an acceleration of 1.60 m/s². We know that the net force acting on the sled is given by:

net force = mass * acceleration

We can rearrange this equation to solve for mass:

mass = net force / acceleration

Since there is no friction, the net force on the sled is equal to the horizontal component of the force exerted by the spring:

mass = Fx / acceleration

Plugging in the values we know, we can find the mass of the sled.

Next, we can use Newton's second law of motion, F = ma, to relate the force exerted by the spring to the displacement x. We know that the force exerted by the spring is equal to the weight of the sled, which can be calculated as:

weight = mass * gravity

where gravity is the acceleration due to gravity.

Since the weight is equal to the force exerted by the spring:

weight = k * x

We can rearrange this equation to solve for x:

x = weight / k

Plugging in the known values, we can calculate the displacement of the spring, which is the amount by which it stretches.