What is the minimum acceleration of the car for this to happen? (Assume no air resistance)
A 2.50kg object is tied to a string. The object is placed in front of a car and the string is tied to the hood ornament. This causes the object to dangle down in front of the car (85.0cm above ground), touching the front of the car (but not touching the ground). The coefficient of kinetic friction between the front of the car and the object is 0.650, while the coefficient of static friction between the front of the car and the object is 0.870. The car begins to accelerate forwards uniformly. At some point during this, the string slips off the hood ornament but the object doesn't slide down the front of the car.
A 2.50kg object is tied to a string. The object is placed in front of a car and the string is tied to the hood ornament. This causes the object to dangle down in front of the car (85.0cm above ground), touching the front of the car (but not touching the ground). The coefficient of kinetic friction between the front of the car and the object is 0.650, while the coefficient of static friction between the front of the car and the object is 0.870. The car begins to accelerate forwards uniformly. At some point during this, the string slips off the hood ornament but the object doesn't slide down the front of the car.
1 Answer
Explanation:
Sum the forces on the object in the vertical direction:
Substitute
Substitute
Sum the forces in the horizontal direction:
The force of the vehicle on the object is equal to the mass of the object multiplied by the acceleration of the vehicle:
Substitute equation [2] into equation [1]:
Solve for the acceleration of the vehicle:
Substitute
