a) The weight of the object can be calculated using the formula: weight = mass x gravitational acceleration. Given that weight = 500N and gravitational acceleration = 9.81 m/s^2, we can find the mass of the object:
500 = mass x 9.81
mass = 500 / 9.81 = 51 kg
b) To calculate the smallest force P needed to push the object upwards, we first need to find the force of friction acting against the object on the slope. This force is given by the formula: friction force = coefficient of friction x normal force. The normal force acting on the object can be calculated using trigonometry:
normal force = weight x cos(20°)
normal force = 500 x cos(20°) = 469.57N
Then, we calculate the force of friction:
friction force = 0.2 x 469.57 = 93.91N
Now, we break the weight of the object into components parallel and perpendicular to the slope. The force parallel to the slope is equal to the sum of the pushing force (P) and the force of friction. This force can be calculated using trigonometry: force parallel = weight x sin(20°). Rearranging this formula, we get:
P + friction force = weight x sin(20°)
P + 93.91 = 500 x sin(20°)
P = 500 x sin(20°) - 93.91
P = 170.54N
Therefore, the smallest force P needed to push the object upwards is 170.54N.
An object is pushed upwards against a slope by a pushing force (P) which forms an angle of 15° with slope. The object weighs 500N, and the slope forms as angle of 20° with the horizontal. The coefficient of friction between the surfaces in contact is 0,2.
Calculate:
a) The mass of the object
b) The smallest force P needed to push the object upwards
1 answer