A weight of 150 pounds is placed on a smooth plane surface which makes an angle of 35 degree with the horizontal. The weight is held by a string parallel to the surface and fastened at the top of the plane. Find the pull on the string.
See previous post: Thu, 7-30-15, 3:28 AM
To find the pull on the string, we need to resolve the weight into its components.
First, let's find the vertical component of the weight. This can be calculated using the formula:
Vertical Component = Weight * sin(angle)
Plugging in the values given, we get:
Vertical Component = 150 pounds * sin(35 degrees)
Vertical Component ≈ 150 pounds * 0.5736
Vertical Component ≈ 86.04 pounds
Next, let's find the horizontal component of the weight. This can be calculated using the formula:
Horizontal Component = Weight * cos(angle)
Plugging in the values given, we get:
Horizontal Component = 150 pounds * cos(35 degrees)
Horizontal Component ≈ 150 pounds * 0.8192
Horizontal Component ≈ 122.88 pounds
Since the weight is held by a string parallel to the surface, the pull on the string is equal to the horizontal component of the weight:
Pull on the String ≈ 122.88 pounds
Therefore, the pull on the string is approximately 122.88 pounds.
To find the pull on the string, we need to resolve the weight into components along and perpendicular to the plane.
First, let's determine the component perpendicular to the plane. We can use the weight and the angle between the weight and the horizontal to find the perpendicular component.
The weight can be broken down into two components: the perpendicular component (W⊥) and the parallel component (W║). The perpendicular component can be calculated using the formula:
W⊥ = W * cos(angle)
In this case, the weight (W) is 150 pounds, and the angle is 35 degrees. Applying the formula, we get:
W⊥ = 150 * cos(35)
Next, let's calculate the pull on the string. Since the weight is held by a string parallel to the surface, the pull on the string will be equal to the parallel component of the weight (W║).
The parallel component can be calculated using the formula:
W║ = W * sin(angle)
Again, substituting the values, we get:
W║ = 150 * sin(35)
Therefore, the pull on the string is equal to W║, which is 150 * sin(35). So, the pull on the string would be the numerical value of 150 * sin(35).